Yes, you should call your doctor and ask for the Free T3 and Free T4.
I might suggest that a doctor who is adjusting medications, based only on TSH, will probably keep you very ill. If he refuses to test FT3/FT4, you might want to think about a different doctor.
That is what I thought. Should I call my Dr and ask him why he did not order them?
You may need the full thyroid blood labs done to see where your Free labs are. Removal of thyroid tissue also does not eliminate the autoimmune issues.